Despite renewed statements of concern by Catholic leaders and lawmakers, the Obama administration is done negotiating and will finalize its plan requiring insurance companies to provide free contraception to women working and studying at religious institutions, President Obama's chief of staff said Sunday.

Jacob Lew told "Fox News Sunday" that the compromise offered last week to address objections by the Catholic Church is clear and consistent with the president's "very deep belief that a woman has a right to all forms of preventive health care, including contraception."

"We have set out our policy," Lew said. "We are going to finalize it in the final rules, but I think what the president announced on Friday is a balanced approach that meets the concerns raised both in terms of access to health care and in terms of protecting religious liberties, and we think that's the right approach."

But Senate Minority Leader Mitch McConnell, R-Ky., said the conversation isn't over yet.

"If we end up having to try to overcome the president's opposition by legislation, of course, I'd be happy to support it and intend to support it," McConnell said on CBS' "Face the Nation."

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"It would be difficult as long as the president is rigid in his view that he gets to decide what somebody else's religion is. I assume he would veto it. But yeah, we'll be voting on that in the Senate. And you can anticipate that that would happen as soon as possible," he said.

On Friday, Obama revised his decision to require all employers to provide contraceptive care after Catholic organizations balked that it is an intrusion on the Church's religious liberty to require it to provide birth control. The president changed the mandate to shift the burden to insurance companies to provide free access to birth control and other forms of contraception.

"No institution, nonprofit institution, that has religious principles that would be violated has to pay for or directly offer these services, but women have access to the kinds of care they're entitled to. We think that's the right approach," Lew said Sunday.

"This is a solution so that they are not providing it, so they're not offering it, they're not paying for it. So women have the choice on their own," Lew added. I think a lot of good work was done and hopefully this will now set the issue to rest."

But Catholic leaders, while first reserving judgment, remain dissatisfied. Late Friday, the U.S. Conference of Catholic Bishops issued a statement declaring the new policy of "grave moral concern" and urged Congress to overturn the regulation.

"Today's proposal continues to involve needless government intrusion in the internal governance of religions institutions and to threaten government coercion of religious people and groups to violate their most deeply held convictions," the bishops said in a lengthy statement.

The bishops noted that the change appears to make no consideration for religious insurers or self-insuring religious employers -- or for religious for-profit employers and secular nonprofit employers.

"In a nation dedicated to religious liberty as its first and founding principle, we should not be limited to negotiating within these parameters. The only complete solution to this religious liberty problem is for HHS to rescind the mandate of these objectionable services," the bishops said.

The conference also reiterated its original objection made to the Department of Health and Human Services last year when it began developing the rule.

"All the other mandated 'preventive services' prevent disease," the bishops wrote, "and pregnancy is not a disease."

But Lew said the policy holds true to the "core principles of our country," which call for respecting religious liberty. He noted that the revision had earned support from liberal Catholics and lay groups.

"The solution that we reached is consistent with those core principles. That's why it got the support of a range of groups from the Catholic Health Association and Catholic Charities to Planned Parenthood," Lew said.

He added that the law isn't just about preventing babies.

"There are many health conditions in women that are affected by whether or not contraceptive health is available," he said.

In defending the mandate, which Lew said the president was authorized to implement under the Affordable Care Act passed by Democrats in Congress in 2009, the chief of staff also argued that shifting the coverage requirement to insurance companies doesn't hurt the bottom line.

"If you were looking at an actuarial projection of the cost of a plan, it costs more to provide a plan without than it does with. This is one of those very rare cases where it actually does not cost the insurance company money to do it," he said.

With the administration fast-tracking the policy -- it had planned to roll out the requirement for employer-provided coverage for contraceptive health care over 13 months, but decided to speed up implementation, Lew said, "because clearly it wasn't helpful to have it lingering out there." -- it may be left to lawmakers -- or a new administration -- to reverse it.

"This is outrageous," said Republican presidential candidate Rick Santorum on NBC's "Meet the Press. "The bottom line is that you have the federal government now saying we're going to give you a right and then say, by the way, we're going to tell you how to exercise that right."

"This thing is a distinction without a difference. It's an accounting gimmick or a fig leaf. It's not a compromise. The president's doubled down," said Rep. Paul Ryan, R-Wis., who said on ABC's "This Week" that the House "absolutely" has the votes to block it.

In a statement issued separately from the conference, Cardinal Donald Wuerl, Archbishop of Washington, said the uproar over the mandate has made clear that Americans believe in upholding the principle of religious liberty.

"Regardless of whether or not they agree with Church teaching on a particular issue, people believe strongly that the government should not force the Church and its institutions to do things it considers morally wrong. Hopefully, the ultimate resolution of this issue will reflect this longstanding American principle. No matter the outcome, we must continue to be vigilant against the encroachment of government on the free exercise of religion," he said.